A Smoothed Particle Hydrodynamics method with approximate Riemann solvers for simulation of strong explosions

A new modification of the Smoothed Particle Hydrodynamics (SPH) method is presented. The performance of the proposed method is checked when used together with Local Lax-Friedrichs (LLF), Harten, Lax, van Leer (HLL) and exact Riemann solvers, and we derive the SPH equations for each applied solver. The validation problems include Sod's problem, Sjögreen test, blast wave tests, and collision of strong shocks problem. On the basis of our results, we conclude that the application of HLL and LLF approximate Riemann solvers is preferable, with LLF solver having a smallest compuational load. The conservative properties of the method are also strong. The linear momentum, the total mass, and the total energy are conserved within machine accuracy for all applied Riemann solvers.